N AS A / TM- 1999-209828

Numerical Analysis of

Transpiration Cooling

Convection/

David E. Glass

Langley Research Center, Hampton, Virginia

Arthur D. Dilley

FDC/NYMA Inc., Hampton, Virginia

H. Neale Kelly

Analytical Services & Materials, Inc., Hampton, Virginia

National Aeronautics and

Space Administration

Langley Research CenterHampton, Virginia 23681-2199

December 1999

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Numerical Analysis of Convection/Transpiration Cooling

David E. Glass*

MS 396, NASA Langley Research Center, Hampton, VA 23681

Arthur D. Dilley _

FDC/NYMA Inc., 1224 N. Wright St. #11, Hampton, VA 23681

"and

H. Neale Kelly ¢

Analytical Services & Materials, Inc., 107 Research Drive, Hampton, VA 23666

Abstract

An innovative concept utilizing the natural porosityof refractory-composite materials and hydrogen coolant toprovide CONvective and TRANspiration (CONTRAN)cooling and oxidation protection has been numericallystudied for surfaces exposed to a high heat flux, hightemperature environment such as hypersonic vehicleengine c0mbustor walls. A boundary layer codc and aporous media finite difference code were utilized toanalyze the effect of convection and transpiration coolingon surface heat flux and temperature. The boundary layercode determined that transpiration flow is able to provideblocking of the surface heat flux only if it is above aminimum level due to heat addition from combustion of

the hydrogen transpirant. The porous media analysisindicated that cooling of the surface is attained withcoolant flow rates that are in the same range as thoserequired for blocking, indicating that a coupled analysiswould be beneficial.

Nomenclature

a = coefficient in Nub = coefficient in Nu

B,, = coefficient for first order effect in permeabilityCp_ = coolant specific heatd = coefficient in finite difference equationDh = hydraulic diameter of the coolant channelG = mass flow rate per unit areah = heat transfer coefficient

i = spacial index in finite difference equationk = thermal conductivityK = permeability

K, = coefficient for second order effect in permeabilityL = thickness of porous mediam = molecular mass

M = molecular weightNu = Nusselt number

AP = pressure difference (P_.h- P_,,n,h)P = pressurePr = Prandtl number

q_op_ = applied heat flux at combustor wallRe = Reynolds numberR, = universal gas constantRH2 = hydrogen gas constantT = temperatureV = velocity of coolantx = spatial coordinate in porous media

Grt_k

= porosity= Boltzmann constant

!u = viscosity

9 = density

Subscripts and Superscripts

avg = averagec = coolant in porous mediach = coolant in coolant channelcomb = combustion chambereft = effective

m = porous medias = surface

v = volumetric, in porous mediawall = conditions at surface of combustor wall

Introduction

Design and trade studies of hypersonic vehicles haveshown significant benefits lor operation at high enginewall and coolant/fuel temperatures. One approach toachieving these operational conditions in enginecombustors has led to the development of a platinum clad

* Aerospace Engineer, Senior Member, AIAAt Senior Research Engineer, mailing address, MS 353X, NASA Langley, Hampton, VA 23681$ Retired

Work was performed while all authors were employed by Analytical Services & Materials. Inc.. 107 Research Drive,Hampton, VA 23666

Mo-50Realloy for theconvectivelycooledstructure.Thisapproachhasbeentakenbecauseof therequirementslot amaterialwithbothhigh-temperaturestabilityandhighthermalconductivitytoaccommodatetheanticipatedhigh heat fluxes. However, these materials are expensiveand the cladding has not been reliable. Because Mo-Rehas poor oxidation resistance, serious problems can resultfrom exposure of the Mo-Re to oxygen should a breachoccur in the cladding.

Cooled refractory composites have been consideredfor nozzles but have not been proposed for combustorsbecause of their relatively low thermal conductivity.Furthermore, the use of convectively cooled refractorycomposites using leak-tight metallic liners in the coolantpassage and oxidation protection surface coatings causeadditional design constraints due to materialincompatibility and thermal expansion differencesbetween the tubes and the liners as well as the external

coating compatibility with the combustor environment,respectively.

f Tlal'_spiring H_- ( dli_lll- CalVin or

t)thcr n_lractory ct)ml_X+tc 1

t_ minimize leakage _lul ha_'k side

Fig. 1. CONTRAN cooling concept.

An innovative concept utilizing the natural porosityof refractory-composite materials and hydrogen coolant to

provide CONvective and TRANspiration (CONTRAN)cooling and oxidation protection has been proposed forsurlhces exposed to a high heat flux, high-temperatureenvironment such as hypersonic vehicle enginecombustor walls. Specifically, the concept relies on thehydrogen coolant to permeate the selectively densifiedrefractory-composite material such as carbon/carbon(C/C) to provide a reliable cooling and oxidationprotection system. The basic CONTRAN concept,which is shown in Fig. I, is based on the fundamentalpremise that the natural porosity of refractory-compositematerials leads to leaks. Though little can be done tocompletely eliminate the leaks, the leak rate can becontrolled through selective densification of therefractory-composite materials. The hydrogen coolantwhich permeates the C/C prevents oxidation, and thetranspiring coolant also significantly reduces the heatflux. Since the transpiration cooling is very effective incooling the structure and it blocks some heat inputexterior to the surface, the very high thermal conductivityrequirements imposed by a pure convective coolingsystem no longer exist. Similarly, the needs tbr

impermeable oxidation protection coatings and leak freecoolant liners are eliminated. An important aspect of theCONTRAN concept is control of the spatial variation ofthe hydrogen permeability through the composite, bothto minimize the coolant leakage out of the back side "andto accommodate the variations in the heating conditionsover the hot surface.

('tx)tanl

weight, lh

40(_)

(_ I

0 _)00

Haynes 188

T s = 22fi(I R

"1"¢ s = 2_(I(I"R

CarNm/cm'bon _

To, s = 21)0_)" R _ _

H2 "_ _' _ _

2(1_)0 4[)o0

Temr, cralu_'. R

Fig. 2. Coolant weight as a function oftemperature for hydrogen and helium coolant.Also shown are design conditions for Haynes

188 and C/C closure door.

Potential benefits of the application of theCONTRAN cooling concept are illustrated in Fig. 2.The particular example shown is for an inlet closuredoor, not a combustor wall panel, and the cooling modeis pure transpiration (with an energy balance for whichwall surface temperature equals outlet coolanttemperature), which is a limiting case of the CONTRANconcept. The heat blocking effects of transpirationcooling are not considered. The closure door isduring re-entry to prevent hot gases from entering theengine, and the expendable coolant, which is dumpedoverboard, represents a direct weight penalty. The "dashedline in Fig. 2 illustrates the reduction in coolant weightpenalty as a function of hot surface temperature where thecoolant temperature is permitted to rise to the surfacetemperature, as it will with transpiration cooling. If thesurface is allowed to rise to -5000°R, no weight penaltyis incurred since no coolant is required. The figure also

presents coolant weight requirements using helium as thecoolant medium to alleviate concerns about external

burning of the hydrogen coolant. Previous enginecontractors' design studies, as shown by the two designconditions (symbols), indicate that the coolant weightpenalty can be reduced by -3000 lb by switching fromthe baseline Haynes 188 alloy door to a C/C door.However, the C/C design is constrained by the 3460°Rlimit imposed by the oxidation protection coatings andthe 2000°R limit imposed by metallic tube liners. Forthe C/C design, an additional 2000 Ib savings canrealized (as shown on the dashed line) with transpiration

coolingbytheeliminationof the2000°Rlimit for thecoolanttubes.

Thelackof serious consideration of transpirationcooling for engine combustors may be ascribed topreconceived concerns about and lack of knowledge of theconcept and the specific application for which it has t'_nproposed. Transpiration cooling has been proposed forthe engine cowl lip and other stagnation regions.However, there has been serious concern about the

transpiring coolant altering the effective aerodynamicshape of the components, the potential detrimental effectsof shock impingement on transpiration coolingeffectiveness, and the unknown effects of combustion of

the transpirant on the cooling process, as well as thepotential impact of that combustion on the inlet andoverall engine performance. Several of these concerns areaddressed in paper.

HL_t gas

('oolanl I1o_

Heat inpul Q_) Thermal hk_cking

Trallspil'ali_lll

(:()liVe!lion - cSnduclion

Fig. 3. Schematic diagram showing aspects ofCONTRAN cooling to he modeled in computer

analysis.

The numerical analysis results presented here utilizedtwo codes to m(xtel the CONTRAN cooling of C/C. Aboundary layer code was used to calculate the effect of thetranspiration cooling on reducing the heat flux at thesurface (effect I in Fig. 3). The porous media codemodeled both the convective cooling in the coolantchannel and the thermal-fluid mechanics of transpirationin the porous media, as illustrated by effects 2 and 3 inFig. 3. The two codes, though not coupled, were usedtogether to demonstrate the feasibility of usingCONTRAN cooling for scram jet engine combustors.

Boundary Layer Analysis

The viscous flow along the C/C surface wascomputed using an implicit finite-difference boundarylayer code. t A binary diffusion model was assumed withinjection of the hydrogen coolant into the freestream gas.The species composition of the gas mixture was

determined using a Gibbs free-energy minimization

procedure. The external flowfield was modeled as a flatplate with either a constant or varying pressure at theboundary layer edge. Injection of coolant was initiated

downstream of the leading edge of the flat plate to permitinjection into a developed turbulent boundary layer. Theheat transfer predicted by the code included bothcombustion and the blocking effect of the hydrogencoolant. In all cases, the boundary layer was assumedattached. Elimination or removal of oxygen at thesurface resulted from burning of the oxygen with thetranspiring hydrogen, not removal of the boundary layer.

?,._a_ | ........ , .... , .... , .... , ....

N Ideclh = 5.8

2000 _ No h_*=_on

L_ ..... w.hi,W:non= [/ :

lsoo _-k :',

_ ',',

1000

.... p . • ,

0 5 10 15 2O 25 30

Aml Dtmn,m (in.)

Fig. 4. Heat transfer rates on a flat plate withand without transpiration cooling.

1000 , , ,

900 -- (pv).. o.o =,J_/mc

800 _ (pv). • 0.01S7 Ib./_/NC

(pv). = 0.0314 Io.?lt211ec

700 _ (pv). • 0.0S4S Ib./lt_lNc

600u

4OO

°= 300

200

100 .

.... [ .... l .... I

O0 5 10 1S 2O

x(_)

Fig. 5. Effect of hydrogen mass flow rate on thesurface heat flux with a pressure gradient.

An analysis of a shock-free flowfield using theboundary layer code is shown in Fig. 4. The figureshows the heat transfer rates with and without hydrogentranspiration. The inflow conditions for this case (Mach5.8) are based upon flight-scale scramjet combustorconditions. The geometry was a flat plate, and aturbulent boundary layer was developed betbre injectionbegins. The spike in the heat transfer with injection wascaused by the immediate burning of the hydrogen coolantand surface oxygen when injection starts. After the

oxygennearthesurfacewaseliminatedbyburningwithhydrogen,theheatingratedropsbelowthenoinjectioncase.Thisresultdemonstratestheblockageeffectof thehydrogentranspiration.

Theboundarylayercodewasalsousedto simulatehydrogentranspirationinto a scramjet combustorflowfieldwithpressuregradientstosimulateshockwaves.Theinflowcondition(Mach4.22)wasfroma pulsefacilitywhichis usedto testsubscalescramjetdesigns.Theshockwavewasme,deledbyvaryingthepressureattheboundarylayeredge.Heattransferresultsfromaparametricstudyof theinjectionratesareshowninFig.5. A sharpincreasein pressureoccursatapproximately9 in., witha smallerincreaseatapproximately13.5in.Injectionof hydrogenstartsslightlyaheadof thefirstshockimpingement.At thelowestinjectionlevel,theheattransferto thesurfacehadactuallyincreasedductothehydrogeninjection.As theinjectionrateincreased,theheattransferwasreducedbelowthenoinjectioncase.

:o2o[I !L

X 11_1

Fig. 6. Effect of hydrogen mass flow rate on theoxygen concentration at the surface.

The reason lbr the increase in heat transfer at low

injection levels is shown in Fig. 6. This figure showsthe axial variation of the oxygen concentration at thesurface. At the lowest injection level, the oxygen wasnot eliminated from the surface and injected hydrogencontinued to burn near the surface. This burning resultedin increased heating rates. At the highest injection level,the oxygen was rapidly removed from the surface and theheating rates decreased. In this case, the burning of thehydrogen occurred away from the surface and the expectedreduction in heat transfer from transpiration cooling wasrealized.

The effect of combustion of transpirant on heattransfer has been validated by changing the compositionof the inflow gas. The heating rates for air and purenitrogen are shown in Fig. 7. The nitrogen inflow casedoes not have a spike in the heat transfer immediately

following the start of injection because of the absence ofoxygen. In this case, the heat transfer drops immediatelyafter the injection begins. After the first shockimpingement, the results with the nitrogen inflow _eslightly below the air inflow case.

tovk. - o.o "-._

----*-'-- (m'). - 0_Ss4s Ib.nl%K, Air Inflow

(pv), • 0.0S4S lb.tl_lmc. N_Ir_,ow

_oo[

a2ooi

_00

100

.... i .... i i ....00 5 10 15

x 4_)2O

Fig. 7. Effect of infh)w gas on the surface heatflux.

|

100

F300 [ -------e------ (pv). • 0.0314 IbJ1121mr..Air Inflow

[ (pV). = 0.0545 Ib.h_/le¢, Air Inflow

(pV). = 0.0545 Ib,./_/_,C, N= Inflow2O0

AQ

-100 _:

8 10 12 14 16 18x (in.)

Fig. 8. Blockage effect of the gas injection onthe surface heat flux.

The blockage effect of the hydrogen injection isshown in Fig. 8. In this figure, the difference in heatingrate due to injection is plotted for several cases consideredin this study. The effects of nitrogen inflow and increasedinjection rates are clearly shown. The boundary layer cxxJcindicates that the pressure gradients due to the shocks donot remove the transpiration flow from the surface andreduce the cooling. Instead, the region where the shocksimpinge experience a significant cooling effect of thetranspiration flow. These results confirm the ability ofthe CONTRAN concept to provide thermal and oxidationprotection using hydrogen transpiration through a porousmedium.

4

Porous Media Analysis

The approach taken in the porous media analysis wasto solve three coupled dif'lbrential equations for the C/C

temperature, the hydrogen temperature, and the hydrogenpressure in the porous media. A general convectionboundary condition was assumed at both boundaries ofthe porous media, i.e., inside the coolant channel and atthe combustor surlace. At the combustor wall surtace,

blocking (a reduction) of the applied heat flux occuneddue to the injection of the hydrogen into the boundarylayer. The permeability and mass flow rate werecalculated in the code. A discussion of the numerical

procedure used for solving the three equations tbr thethree unknown (T,,, T_, P) as well as the porous media(C/C) permeability and the coolant (hydrogen) mass flowrate tbllows.

_ qappl

x=g !_:ii_ii!ii)_!;ii_ii!i!i,!!)::i_i:!ii!,!i.iil):Tm -- p°rous media tcmpcrarar¢

i':_i')':_:!.i'(:!_i!'_'!::!,ii:_!_i'.:,)i! Tc -- coolant te_

X=0 4, hv = volumetricheat transfer

_1_ eoef'fieient

Geh = 255 lb/'m2-s _" hch = coolant eharmel heattransfer coefficient

840"F_< Teh _<1558"F

3648 psi > Peh ->2643 psi

Fig. 9. Schematic diagram of the porous mediaand the nomenclature and channel coolant

values used in the thermal analysis.

Porous Media Temperatures and CoolantTemperatures and Pressures

The first step was to calculate the porous mediatemperature and coolant temperature and pressure. Thisrequired the solution of three differential equations forthree variables, Tin, T_, P. A schematic diagram of theporous media with the channel coolant flow rate,temperature, and pressure is shown in Fig. 9.

A I-D energy balance on the porous media results inthe fbllowing equation:

d2Tm h_--(Tin-To)= 0

dx 2 keg

where Tm is the porous media temperature, T_. is the

coolant temperature, hv is the volumetric heat transfer

coefficient in the porous media, and k,.a- is the effective

thermal conductivity of the porous media as measured by

treating the porous media as a porous solid with nocoolant.

The volumetric heat transfer coefficient, h_, is

calculated according to an empirical formula for flow in aporous media and has units of Btu/inLs-°R. The porous

media flow Nusselt number is defined by Florio-" as

Nu, = a Re b

where a = 2.22 x 10 -_', b = 0.703, and the Reynoldsnumber, Re, is defined as

Re = - P_' B_°5dP3

].Ice dx

The coolant density is detined as p,. and the coolant

viscosity is defined as la,.. The porosity is given by E.

The coefficient B,, is the coefficient of the first order

effect term in the permeability K (de_ribed

subsequently).

The pressure of the coolant in the porous media isthe second variable that must be obtained, and it is

obtained from the solution of a first order differential

equation given by

dP_ p G c

dx p B

where G_ is the mass flow rate per unit area and theviscosity and density are functions of temperature and

pressure.

Once Nu, is calculated, h_ is obtained from

h,- Nu'kcBo

where k, is the thermal conductivity of the coolant. The

volumetric heat transfer coefficient, h,, was calculated at

each node as a function of temperature.

The boundary conditions are given as

h_h(T_h-Tm) = - k_,, dT,,, atx=0dx

dT,,,q_ppl= - k,,t,_ dx at x = L

where qappl is the applied beat flux at the boundary x = L.

The coolant heat transfer coefficient, h_.h, wascalculated from the Nusselt number |or turbulent flow.The coolant channel Nusselt number is defined as 3

Nu_h=0.027Re4/5prl/3 ["_"] I/4

LP_J

where P,'h and ltl_ are the coolant viscosity at thetemperature of the coolant in the coolant channel and at

the cold surfacetemperatureof the porousmedia,respectively.

OncetheNusseltnumberwascalculated,thecoolantheattransfercoefficientwasobtainedfrom

h_h-NuchkcDh

whereDh is the hydraulic diameter of the coolant channel.

The third equation to be solved gives the coolanttemperature distribution. An energy balance on thecoolant yields

dT h v (Tin _To) : 0dx GcCpc

where Cp_ is the coolant specific heat. The remainingIxmndary condition that was used is that the coolanttemperature at x = 0 equals the temperature of the coolantin the channel, T_.(0) = T_.h. The coolant and porousmedia temperatures are coupled and must be solvedsimultaneously. The coolant temperature can be solvedexplicitly, with the coolant temperature in finitedifference tbrm being

T_.i = (d Ax Tm,i + Tc.i.])/(I + d Ax)where

and i is the nodal index that increases with x.

Permeability

The permeability K is a function of both temperatureand pressure and is defined as

B,, l_,,g + 4K= " "'_ 7 K,,V_,_

P'avg

The coefficients K,, (4.094 x 10-8 in.) and B,, (4.96 x 10-

13 in 2) arc constants that are determined when obtaining

the permeability as a function of temperature and

pressure. The values used here were obtained from

unpublished data tbr C/C resulting from work performed

by Oak Ridge National Laboratory for NASA LangleyResearch Center. The average dynamic viscosity,

la,,_,(I.039x10 -6 Ibm/in-sec) is defined to be the

viscosity at the average temperature. T_,,_ = 1300°F.

The average pressure in the porous media is defined,'it

Pch + Pcomb

P_ - 2

The average velocity in the porous media is defined as

Va_ _ =

where _c is the Boltzmann constant (1.3803x10 -23

J/molecule K) and m is the molecular mass (3.34522x 10-

27 kg/molecule).

Mass Flux

The mass flow rate per unit area, G_, can becalculated using an equation originally proposed byBond 4, where the temperature, T,v_, is the averagetemperature of the porous media, L is the thickness ofthe porous media, M is the molecular weight of thecoolant, and R, is the universal gas constant.

KAP MG c -

L RuTavg

The above equation uses the average temperature of theporous media and the pressure difference between thecoolant channel and the combustor. The differential

equation used earlier to calculate the coolant pressure inthe porous media uses the mass flux calculated here alongwith temperature and pressure dependent coolantproperties throughput the porous media.

The porous media temperatures were solved usingfinite differences. They were then used to calculate the

coolant temperatures and pressures. The coolanttemperatures and pressures were then used to recalculatethe porous media temperatures until convergence wasreached.

Results and Discussion

A parametric study was performed using the finitedifference code described above to evaluate the effect of

the transpiration mass flow rate (which is a function of

permeability and pressure) and heat flux on the surfacetemperature of the heated surface. The C/C thermalconductivity and the hydrogen coolant viscosity andthermal conductivity are temperature dependent andcalculated at each node. The hydrogen coolant specificheat and density are both pressure and temperaturedependent. The convection coefficient in the channel wascalculated numerically, and the channel was assumed tohave a square cross section 0. I in. by 0.1 in. with a massflux of 2.55 Ib/in2-s. The thickness of the porous media,L, was assumed to be 0.1 in. Since the coolant in thecoolant channel was heated along the flow path, two

different coolant temperatures were used, 840°F and1560°F. The temperatures represent the inlet and outletcoolant temperatures for a typical combustor. Thecorresponding coolant pressures were 3648 psi and 2643

psi. Thesecoolanttemperaturesandpressuresarerepresentativeof pure convectioncooling. Theconvectioncoefficientforthecoolantintheporousmediawasalsocalculatednumerically.A sketchof thegeometryandnomenclatureusedin thethermalanalysisisshowninFig.9.

Ts. °F

4000

¸: -qappl 60(J Btlff|l" s

2500

2000 _ __,,_...,____ppl - 40() BIU/)I _ s

150O

1000 _ qappl = 2(XI Bm/fi2-s

50O

{I I I I I I

O,(X)O0 0.0005 0,0010 0.0015 0.00211 0,0025

Transpiration mass flux. Ib/in2-s

Fig. 10. Combustion wall surface temperature asa function of transpiration mass flux and

applied surface heat flux at the entrance to thecoolant channel (coolant at 840°F and 3648

psi).

In the current analysis, the sur[hce temperature isallowed to reach a value dependent on all the conditionsof the problem. The applied heat flux is given, but thesurface temperature and transpiration flow rate arecalculated. Iterations would then be required between theporous media solution and the boundary layer solutionwhich computes the applied net heat flux if a coupledanalysis for all three effects in Fig. 3 were desired.

In Fig. 10, the surface temperature of the C/C isplotted as a function of the transpiration mass flow rateand the applied surface heat flux for the conditions at theentrance of the coolant channel, with the channel coolant

at a temperature of 840°F and a pressure of 3648 psi.The surface heat flux is assumed to include any blockingeffect of the transpiring coolant. The porous mediaanalysis does not calculate the magnitude of the blockingeffect of the transpiration, but utilizes the net heat fluxapplied to the surface (which could be calculated by the

boundary layer code). The surface temperature wascalculated for fbur different heat fluxes, ranging from 200Btu/ft2-s to 800 Btu/ft2-s. The mass flow rate is a

function of the pressure, temperature, and permeability.Since the pressures and temperatures are determined aspart of the analysis, only the permeability needs to bevaried to obtain the range of mass fluxes, G_.. Thepermeability was varied by varying the coefficients 13,,and K,,, The porosity and effective thermal conductivityof the porous media were not changed in this analysis.(Note that h,. is also a strong function of mass fluxpermeability.) From the figure, it can be seen that as the

mass flow rate is increased, the surface temperatureappears to become insensitive to transpiration mass flowrate, indicating that for high flow rates, the wall surfacetemperature essentially becomes a function of appliedheat flux only.

4000

3500

3000

Ts, 'F

250()

2OO0

1500

too0

O.0OOO

. _ Btu/fl2-s

2°s

_._appl = 40(1 BttL/ft2-s--J

qappl = 20() Btu/ft2-s-=-_

I I I I

0.0005 0.0010 0.0015 0.0020

Transpiration mass flux, Ib/in2-s

Fig. 11. Combustion wall surface temperature asa function of transpiration mass flux and

applied surface heat flux at the coolant exit tothe combustor (coolant at 1558°F and 2643

psi).

In Fig. l l, the surface temperature of the C/C isplotted as a function of the transpiration mass flow rateand the applied surface heat flux lot the conditions at theexit of the coolant channel, with the channel coolant at a

temperature of 1558°F and a coolant pressure of 2643psi. Again, the surface temperature is calculated for fourdifferent heat fluxes, ranging from 200 Btu/ft-_-s to 800Btu/ft2-s. From the figure, it can be seen that as themass flow rate is increased, the surface temperatureappears to become less sensitive to mass flow rate.

Here, the wall surface temperatures are higher than for theentrance conditions, due both to the higher coolanttemperature and the lower pressure, which results in alower mass flow rate for a given permeability.

The results from Fig. 10 and Fig. II indicate thatC/C permeabilities that result in transpiration fluxesgreater than 0.(X)2 Ib/in2-s result in little further reduction

of surface temperature at the given heat flux levels. Themass fluxes used for blocking in the boundary layeranalysis were up to 0.0545 Ib/ft-_-s, or 0.00038 lb/in-'-s.

The mass fluxes required to reduce (block) the heat flux atthe surface calculated from the boundary layer analysis m-ethus at levels where the wall temperature is sensitive tomass flux variations. This indicates that coupling of thetwo analyses would be beneficial.

Concluding Remarks

A convection/transpiration cooling technique lbrcooling engine comhustors was numerically studied

usingbotha boundarylayercodeanda porousmediaanalysis.Theboundarylayeranalysisdeterminedthattranspirationcoolingcanblocktheheatflux from thecombustor.Theporousmediaanalysisindicatedthatvalucsof thc surfacetemperaturesarereachedwhereincreasesin the coolantflow rate (controlledbypermeability)havelittle furthercoolingeffecton thesurfacetemperature.Theboundarylayerandporousmediaanalysisshouldbecoupledto furtherinvestigatethefeasibilityof this convection/transpirationcoolingtechniqueforhypersonicvehiclecombustorwalls.

Acknowledgment

The authors greatly appreciate the support of the AirForce Research Laboratory at Wright Patterson Air ForceBase, OH for support of this work under a Phase I SBIR,Contract No. F33657-93C-2227. The assistance of Dr.

Clay Anderson of NASA Langley Research Center inrunning the boundary layer code is greatly appreciated.

Reference

_Anderson. E. C. and Lewis, C. H., "Laminar or

Turbulent Boundary-Layer Flows of Perfect Gases orReacting Gas Mixtures in Chemical Equilibrium,"NASA CR- 1893, 197 I.

2FIorio, J., Jr., Henderson, J. B., Test, F. L., and

Hariharan, R., "A Study of the Effects of theAssumption of Local-Thermal Equilibrium on theOverall Thermal-Induced Response of a Decomposing,Glass-Filled Polymer Composite," hlternational Joun2alof Heat and Mass Transfer, Vol. 34, No. I, pp. 135-147,1991.

_Incropera, F. P., and DeWitt, D. P., Fundamentals ofHeat and Mass Tvanst;er, John Wiley & Sons, New York,1990.

_Bond, R. L., editor, Porous Carbon Solids, Academic

Press. New York, 1967.

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Washington, DC 205031. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED

December 1999 Technical Memorandum

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

Numerical Analysis of Convection/Transpiration Cc×_ling

6. AUTHOR(S)

l)avid E. (;lass

Arthur D. Dille)

H. Neale Kell)

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Langley Research (?enterHampton, VA 23681-2199

9. SPONSORING/MONITORINGAGENCYNAME(S)ANDADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

242-33-03-20

8. PERFORMING ORGANIZATIONREPORT NUMBER

L-17915

10. SPONSORING/MONITORINGAGENCY REPORT NUMBER

NASA/TM- 1999-209828

11.SUPPLEMENTARYNOTES

12a. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified-Unlimited

Subject Category 34 Distribution: Standard

Availability: NASA CASI (301) 621-0390

12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

An innovative concept utilizing the natural porosity of refractory-composite materials and hydrogen coolant to

provide CONvective and TRANspiration (CONTRAN) cooling and oxidation protection has been numerically

studied for surfaces exposed to a high heat flux, high temperature environment such as hypersonic vehicle

engine combustor walls. A boundats layer code and a porous media finite difference code were utilized to

analyze the effect of convection and transpiration cooling on surface heat flux and temperature. The boundary

layer code determined thai transpiration flow is able to provide blocking of the surface heat flux only if it is

alxwe a minimum level due to heat addition from combustion of the hydrogen transpirant. The porous media

analysis indicated that cooling of the surface is attained with coolant flow rates that are in the same range as

those required for blocking, indicating that a coupled analysis would be beneficial.

14. SUBJECT TERMS

Active cooling; carbon/carbon: transpiration

17. SECURITY CLASSIFICATION

OF REPORT

Unclassified

1_. 5P...II_UHITY GLA,551FICAT[UNOF THIS PAGE

Unclassified

lg. ,_E,f,,;UHI1-Y GLA,_51PICATIONOF ABSTRACT

Unclassified

15.NUMBEROFPAGES15

16. PRICE CODE

A0320. LIMIIA]IE)N

OF ABSTRACT

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:Standard I-orm 298 (Rev. 2-89)Prescribed by ANSI Std Z-39-18298-102